Solve for $x$: $\frac{3x - 1}{4x-4} = \frac23$.
Solution: Multiplying both sides by $4x-4$ and by 3 gives $3(3x-1) = 2(4x-4)$.  Expanding the products on both sides gives $9x-3 = 8x - 8$.  Subtracting $8x$ from both sides $x -3 = -8$ and adding 3 to both sides gives $x = \boxed{-5}$.